Question

Arata ca nr A=2^2003+3^2003+4^2004+5^2003+6^2003+7^2003 nu este patrat perfect. Explicit pls

Answer 1

2²⁰⁰³ +3²⁰⁰³ + 4²⁰⁰⁴ +5²⁰⁰³ +6²⁰⁰³ +7²⁰⁰³

U (2²⁰⁰³)= U( (2⁴)⁵⁰⁰ *2³) = U(16*8)= U(6*8)= U(48)= U(8)

U (3²⁰⁰³)= U( (3⁴)⁵⁰⁰ *3³) =U(81*27)=U(1*7)= U(7)

U (5²⁰⁰³)= U(5)

U (6²⁰⁰³)= U( 6)

U (7²⁰⁰³)= U( (7⁴)⁵⁰⁰ *7³) =U(2401*343)= U(1*3)= U(3)

U( 4²⁰⁰³)=U(4⁴)⁵⁰⁰*U(4³) = U(256)*U(64)= U(6*4) =4

U(8)+U(7)+U(5)+U(6)+U(3)+U(4)=U(8+7+5+6+3+4)=U(33)= U(3)

Ca sa fie patrat perfect un numar trebuie sa aiba ultima cifra: 0, 1, 4, 5, 6, 9.
La a dunarea noastra ultima cifra este 3.
Deci nu este.


Vezi ca pe 4 l-am lasat la urma, dar asta nu schimba nimic la calcul.