i

9

66 ] COUNTEREXAMPL E T O EULER' S CONJECTUR E 107 9

2 .

F . P . Ramsey , On a problem of formal logic, Proc . Londo n Math . Soc . (2 )

3 0 (1930) , 264-286 .

DARTMOUT H COLLEG E

COUNTEREXAMPL E T O EULER' S CONJECTUR E

O N SUM S O F LIK E POWER S

B Y L . J . LANDE R AN D T . R . PARKI N

Communicate d b y J . D . Swift , Jun e 27 , 196 6

A direc t searc h o n th e CD C 660 0 yielde d

27

5

+ 84

5

+ HO

5

+ 133

6

- 144

5

a s th e smalles t instanc e i n whic h fou r fifth power s su m t o a fifth

power . Thi s i s a counterexampl e t o a conjectur e b y Eule r [l ] tha t a t

leas t n nth power s ar e require d t o su m t o a n nth power , n>2.

REFERENC E

1 .

L . E . Dickson , History of the theory of numbers, Vol . 2 , Chelsea , Ne w York ,

1952 ,