Question

Need help on this question from Math theory. Only answer if you are certain it is correct. Thank you!

5. Prove that 7|(32n – 2”) for every nonnegative integer n.

Answer 1

Leen 9. Prove that 71 (327_2") for every non negative integer ni E Ans! Here we are going to brove the's relation rathematical induction . since here we have to prove the's relation for every non- negative integer n then first take nzol since a non- negative integer is weiter zero on fosili've shteger]. and 710. *. ?(3*- z) for nao. Next, for nel 2n 3 – 2 = 322 -9-2 = 7 : 7(32" 2") for nam statement that the is that is fon KEN true Assume n=k fori. - m fon IN 2K K 3 - - 2 = net w statement e Now, we are going to prove that the is true fork + l isis debesu 32(6+1)_ *Din can be 2 *32 – 2*+! (: antya , at) statement is true for are . we going to use the o. relation

From the equ o we have 22 _ QK = rm for some men m K Ronsomo m CN, Next, 3KI)_ 2k+I CY 3 (7m+gK)323*,- [ from equation @7 de 7m32 z , ga--22 - 63m + 2*( 32-2) I talia = 7.9m 7 7ozk! Ĉ235-2= 7) - 7 ( 9m + 2") motor! Let am + 2 = in for some NEN 22(x+1) _ z kt! = 70 for some NEN 22(k+1) + devisble by 7 sh o the statement is true nd trueth implies for n=o. I. that n=k+1 he for nak 1 also true. without So, the statement 71(32"-12") true for all non-negative integer is n.