Find a way

Number Theory Level 2

Can you make the following two equations true?

$a + b + c^2 = 2025$

$a^2 - b^2 = 2025$

Given that $a, b$ and $c$ are integers.

Yes No

1 solution

Munem Shahriar
Nov 24, 2017

Here's one way to do it:

For $a = 1013,$ $b = 1012$ and $c = 0$

$1013 + 1012 + 0^2 = 2025 \longrightarrow \color{#20A900} \text{True}$

$1013^2 - 1012^2 = 2025 \longrightarrow \color{#20A900} \text{True}$