The New York City Department of Education may be stumped by a $2.1 million Medicaid math problem.

U.S. Attorney for the Eastern District Loretta Lynch joined in today on a 5-year-old whistleblower case that alleged the cash-strapped New York City Department of Education illegally billed Medicaid — the health insurance program for the nation’s poor —to the tune of nearly $700,000 for counseling services it never provided. Lynch is requesting no less than $2.1 million in repayments, fees and other costs.

The Medicaid program is set up to award the department $223 a month for each student who receives counseling services at least twice in a given month. The state and federal Medicaid programs split the costs, leaving both ends on the hook for $111.50 per student per month.

The federal complaint, filed last Friday in New York’s Eastern District Court, alleged that the city was submitting claims not just for the students that received the required two or more services in a month, but all Medicaid-eligible students in schools for particularly troubled or mentally handicapped students.

“We have not received the complaint and cannot address the specific allegations. However, the Department of Education takes counseling services for special needs students very seriously and cooperated with the U.S. Attorney’s investigation,” read a statement provided by Thomas Crane, Chief, General Litigation Division of the New York City Law Department which responded on behalf of the city Department of Education.

“We disagree with any assertion that the DOE engaged in misconduct and will respond appropriately to the complaint.”

The complaint cited one example in which the city billed Medicaid for 17 months worth of services between 2001 and 2003, yet the city was unable to prove that the student received the required two visits in any month.

Between 2001 and 2004, the complaint states, nearly 8,000 of the city’s troubled and handicapped students in District 75 schools — which specialize in children with special needs — received counseling services for which the city billed Medicaid over 86,000 times. The U.S. Attorney alleges that the required number of services were not provided for a “substantial number of months.” In the 2001-2002 school year alone, the complaint alleges, more than 12 percent of all claims were illegal, and while the department knew of these issues, it did nothing to fix the problem.

“We will vigorously investigate and prosecute allegations of fraud on federal programs, especially in programs where the intended recipients of services are vulnerable children with special needs,” said Lynch in a press release.

This is not the only Medicaid-related problem facing the department. Just three years ago, the city agreed to repay Medicaid $100 million for improper billings in the 1990s. A July report from the New York City Comptroller found that the Department of Education overestimated Medicaid reimbursements it would receive in its 2012-2013 budget by another $100 million. And at a March City Council hearing, councilmembers grilled department officials for failing to secure tens of millions of outstanding — and lawful — Medicaid funds for services rendered in city schools.

“This is totally unacceptable by anyone’s standard. The DOE has been on notice since 2005 that they have to improve their documentation and claim procedures,” Education Committee Chairman Robert Jackson said at a hearing earlier this year. “They should have been more prepared by now.”

In 2011, the New York State Office of the Medicaid Inspector General identified more $220 million in improper billings, $1.4 million of which came from audits of the state’s school districts. It is unclear whether the state will seek damages in the suit.