Question

Eu trebuie sa arat ca N=111ori111+222ori222+333ori333+444ori444+555ori555-12345 nu este patrat perfect

Answer 1

$N=111*111+222*222+333*333+444*444+555*555-12345 \\\\N= 111^2+ 2*111*2*111+...+5*111*5*111-12345 \\\\ N=111^2+4*111^2+9*111^2+16*111^2+25*111^2-12345 \\\\ N=111^2(1+4+9+16+25)-12345 \\\\ N= 12321*55-12345 \\\\ N=677655-12345 \\\\ \boxed{N=665310-nu \ este \ p.p}$