show that if 5^(3n) +5^(2n) +5^n +1 is divisible by 13, then n (∈ N) is not a multiple of 4.


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
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

	$t h a n k y o u v e r y m u c h s i r .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum