show-that-if-5-3n-5-2n-5-n-1-is-divisible-by-13-then-n-N-is-not-a-multiple-of-4-

Question Number 122651 by mathocean1 last updated on 18/Nov/20

s h o w t h a t i f

5^{3 n} + 5^{2 n} + 5^{n} + 1 i s d i v i s i b l e b y

13, t h e n n (\in N) i s n o t a

m u l t i p l e o f 4 .

Answered by mindispower last updated on 18/Nov/20

p \Rightarrow q \Leftrightarrow \bar{q} \Rightarrow \bar{p}

l e t n = 4 k

5^{4} = 625 = 13.48 + 1

5^{4} = 1 [13]

\Rightarrow 5^{3 (4 k)} + 5^{2 (4 k)} + 5^{4 k} + 1 \equiv {(1)}^{3 k} + 1^{2 k} + 1^{k} + 1 \equiv 4 [13] \neq 0 [13]

Commented by mathocean1 last updated on 18/Nov/20

t h a n k y o u v e r y m u c h s i r .