That's got to be a fibonacci number.

Number Theory Level 4

find the no.of ordered pair of integers $(a,b)$ such that -

$a^{2} + b^{2} = 1126478964579$

also note they can be negative.

1 solution

Rohit Kumar
Feb 18, 2015

note that $1126478964579$ leaves a remainder of $3$ when divided by four.

and all perfect squares leave a remainder $0$ or $1$ when divided by four.

so, the maximum remainder that their sum can leave is $2$ .

hence no solutions.

Why was the name of the problem "That's got to be a fibonacci number"?

Anik Mandal - 6 years, 3 months ago

Just to confuse.

Rohit Kumar - 6 years, 3 months ago