Question

111^2+222^2+333^2+444^2+555^
2-12345 nu este patrat perfect?Se se arate

Answer 1

111^2+222^2+333^2+444^2+555^
2-12345 =

= 111^2+(2×111)^2+(3×111)^2+(4×111)^2+(5×111)^2 - 12345 =

= 111^2+2^2×111^2+3^2×111^2+4^2×111^2+5^2×111^2 - 12345 =

= 111^2 × (1+2^2+3^2+4^2+5^2) - 12345 =

= 111^2× (1+4+9+16+25) - 12345 =

= 111^2 × 55 - 12345 =

= 12321 × 55 - 12345 =

= 677 655 - 12 345 =

= 665 310 nu este p.p

se afla intre doua p.p
810^2 si 820^2