$a^2+b^3=c^4$

Number Theory Level 3

True or False ?

a,b,c

are three positive integers such that

a^2+b^3=c^4

then

c

is always a multiple of

3

True False

3 solutions

David Vreken
Jun 13, 2018

Another counter-example is $196$ , since $35672^2 + 588^3 = 196^4$ .

Vimay MarCisse
Jun 13, 2018

Another counter-example could be 2 as

2^4 = 4^2 + 0^3

16 = 16 + 0

You're right : I edited slightly the problem to avoid stumbling directly onto trivial counter-examples.

Romain Bouchard - 2 years, 12 months ago

Romain Bouchard
Jun 13, 2018

A counter-example could be $35$ as $35^4 = 1176^2 + 49^3$ .