Question

Demonstrati ca pt orice n,nr natural, b=2 la puterea n +3 la puterea n+1 +5 la puterea n+2 +7 la puterea n+3 ,nu este patrat perfect

Answer 1

intr-adevar pentru n=4k+2

u(2^n)=u(2^4k*2^2)=u(2^2)=u(4)=4

u(3^n+1)=u(3^4k+3)=u(3^3)=7

u(5^n+2)=u(5^4k+4)=u(5^4)=5

u(7^n+3)=u(7^4k+5)=u(7^5)=7

b=2^n+3^n+1+5^n+2+7^n+3=u(4+7+5+7)=u(23)=3=>b nu este patrat perfect)

u=ultima cifra