Hi,

Whilst meandering through integers that fit the equation

$\displaystyle a^2+b^2=2c^2$

I came across this curious result

$\displaystyle 1^2+7^2=2(5^2)$

$\displaystyle 11^2+77^2=2(55^2)$

$\displaystyle 111^2+777^2=2(555^2)$

I went as far as 16 digits and it still holds true.

$\displaystyle 1111111111111111^2+7777777777777777^2=2(5555555555 555555^2)$

I stumped when it comes to figuring a reason for the repetion though.

Any ideas anyone?

Thanks

Pro