Boris Johnson has put his faith in optimism to find technological solutions to prevent a hard Irish border if he becomes prime minister, as the DUP impressed on him the need to resolve the issue of the backstop to keep their support.

Writing what is likely to be his final Daily Telegraph column before entering Downing Street on Wednesday, Johnson used the example of the 50th anniversary of the moon landings to argue for a “can-do spirit” in tackling the Brexit impasse.

“If they could use hand-knitted computer code to make a frictionless re-entry to Earth’s atmosphere in 1969, we can solve the problem of frictionless trade at the Northern Irish border,” Johnson wrote in a column that gave no specifics on how this could be done.

“There is no task so simple that government cannot overcomplicate if it doesn’t want to do it. And there are few tasks so complex that humanity cannot solve if we have a real sense of mission to pull them off.”

He added: “It is time this country recovered some of its can-do spirit. We can come out of the EU on 31 October, and yes, we certainly have the technology to do so. What we need now is the will and the drive.”

Voting for Theresa May’s successor closes on Monday. With Johnson the odd-on favourite to defeat Jeremy Hunt in the race when the result is announced on Tuesday, the backstop insurance policy for the Irish border is shaping up to be a key part of his first weeks in power.

Johnson has promised to entirely ditch the backstop, the arrangement negotiated between May and the EU under which Northern Ireland would stay in the customs union and much of the single market if there was no deal on border and security issues following the end of the Brexit transition period.

Quick guide What is the Brexit ‘backstop’? Show Hide What is the original ‘backstop’ in the withdrawal agreement? Variously described as an insurance policy or safety net, the backstop is a device in the withdrawal agreement intended to ensure that there will not be a hard border between Northern Ireland and the Republic of Ireland, even if no formal deal can be reached on trade and security arrangements. It would mean that if there were no workable agreement on such matters, Northern Ireland would stay in the customs union and much of the single market, guaranteeing a friction-free border with the Republic. This would keep the Good Friday agreement intact. Both the UK and EU signed up to the basic idea in December 2017 as part of the initial Brexit deal, but there have been disagreements since on how it would work. The DUP have objected to it, as it potentially treats Northern Ireland differently from the rest of the UK, creating a customs divide in the Irish Sea, which is anathema to the unionist party. Hardline Tory Eurosceptics also object to it, as they perceive it to be a trap that could potentially lock the UK into the EU’s customs union permanently if the UK & EU cannot seal a free trade agreement. That would prevent the UK from doing its own free trade deals with nations outside the bloc. What was added to May’s withdrawal agreement? Joint interpretative instrument

A legal add-on to the withdrawal agreement was given to Theresa May in January 2019 to try to get her deal through the UK parliament. It gives legal force to a letter from Jean-Claude Juncker and Donald Tusk, the presidents of the commission and council. This stated the EU’s intention to negotiate an alternative to the backstop so it would not be triggered, or, if it was triggered, to get out of it as quickly as possible. Unilateral statement from the UK This set out the British position that, if the backstop were to become permanent and talks on an alternative were going nowhere, the UK believes it would be able to exit the arrangement. Additional language in political declaration This emphasises the urgency felt on both sides to negotiate an alternative to the backstop, and flesh out what a technological fix would look like. However, it failed to persuade the attorney general, Geoffrey Cox, who said that while it ‘reduces the risk’ of the UK being trapped in a backstop indefinitely, it does not remove it. What happens next? Boris Johnson declared the Northern Ireland backstop ‘dead’ during his leadership campaign, and promised to throw it out of any deal he renegotiated with the EU. The EU has repeatedly stated that it will not reopen the withdrawal agreement for renegotiation. Daniel Boffey, Martin Belam and Peter Walker

However, the EU insists it cannot be removed. On Sunday, the Irish deputy prime minister, Simon Coveney, said it was “not a reasonable ask” to remove an integral element of the withdrawal agreement simply because of political needs in Westminster.

Johnson has argued technology could be used to implement a frictionless border. In his Telegraph column on Monday, he condemned the “technological pessimists” who said this was impossible in the available time, adding: “It is absurd that we have even allowed ourselves to be momentarily delayed by these technical issues.”

Jeffrey Donaldson, the DUP MP who is the party’s chief whip at Westminster, said he believed technology could “play a part in addressing this issue”, but warned that the timescales appeared difficult.

“I don’t know whether there will be enough time between now and the deadline in October to get agreement with the EU on what that technology would look like,” he told BBC Radio 4’s Today programme.

It might be possible to complete the task before the end of the Brexit transition period at the end of 2020, Donaldson added. “But we would have to have agreement with the EU on this, otherwise we’re looking at a no-deal situation, and our preference is we leave the EU with a deal. But that means finding a way to address the concerns around the backstop.”

While the DUP’s confidence-and-supply arrangement with the Conservatives would still be in place if Johnson took over, there would be some renegotiation, Donaldson noted.

He said: “We’re about to enter phase two of the confidence and supply agreement, and we will of course be negotiating the arrangements for the next stage of our support for the government.”

Speaking on Talk Radio, the former Brexit secretary Dominic Raab, who is likely to return to the cabinet under Johnson, also called for “a bit more optimism about the enterprise we’re embarked on”.

A change of PM should make a big difference on Brexit, Raab said. “Some of the challenges remain the same, but the difference is, first of all, we had a prime minister who has resigned because the deal hit the buffers and clearly cannot get through parliament.

“That is a fact for the UK and the EU. Secondly, if Boris wins, but I’m reasonably confident we’ve got a prime minister that will stick to the plan of saying we either get a deal that is acceptable to the UK or we’ll leave on WTO terms.”