If , 7^( n) ≡^(10) 7^( 19) then find the 1st digit of the numer , 8^( n+4) .


Question and Answers Forum

All Questions Topic List
Set Theory Questions
Previous in All Question Next in All Question
Previous in Set Theory Next in Set Theory
Question Number 182718 by mnjuly1970 last updated on 13/Dec/22

$If, 7^{n} \overset{10}{\equiv} 7^{19}$ $t h e n f i n d t h e 1 s t d i g i t$ $o f t h e n u m e r, 8^{n + 4} .$
Commented by JDamian last updated on 13/Dec/22
"1st digit" is the right-most one?
Commented by mnjuly1970 last updated on 13/Dec/22

$y e s s i r$ $e x a m p l e . . . 1234 \overset{10}{\equiv} 4$
Commented by Rasheed.Sindhi last updated on 13/Dec/22

${W h a t}^{'} s r e l a t i o n b e t w e e n m & n ?$ $I s m = n ?$
Commented by mnjuly1970 last updated on 13/Dec/22

$y e s$
	Answered by TheSupreme last updated on 13/Dec/22
	$n=19 a_n ={a:8^n ≡_(10) a} 8^1 =_(10) 8 8^2 =_(10) 4 8^3 =_(10) 2 8^4 =_(10) 6 8^5 =_(10) 8 8^(5k+i) ={8,4,2,6,8} 8^(19+4) =_(10) 2$
	$n = 19$ $a_{n} = {a : 8^{n} \equiv_{10} a}$ $8^{1} =_{10} 8$ $8^{2} =_{10} 4$ $8^{3} =_{10} 2$ $8^{4} =_{10} 6$ $8^{5} =_{10} 8$ $8^{5 k + i} = {8, 4, 2, 6, 8}$ $8^{19 + 4} =_{10} 2$
	Answered by Rasheed.Sindhi last updated on 14/Dec/22

	$\underline{MOD 10}$ $7^{2} = 49 \Rightarrow 7^{2} \equiv 9$ $7^{2} . 7 \equiv 9.7 = 63 \Rightarrow \begin{matrix} 7^{3} \equiv 3 \end{matrix} . . . i$ $7^{3} . 7 \equiv 3.7 = 21 \Rightarrow 7^{4} \equiv 1$ ${(7^{4})}^{k} \equiv 1^{k} \Rightarrow \begin{matrix} 7^{4 k} \equiv 1 \end{matrix} . . . . i i$ $i \times i i : \begin{matrix} 7^{4 k + 3} \equiv 3 \end{matrix}$ $7^{n} \equiv 7^{19} = 7^{4 (4) + 3} \equiv 3 \equiv 7^{4 k + 3}$ $n = 4 k + 3$ $\underline{8^{n + 4} = 8^{4 k + 3 + 4} = 8^{4 k + 7} = ?}$ $8^{2} \equiv 4$ $8^{3} \equiv 2 . . . . i i i$ $8^{4} \equiv 6 . . . . i v$ $8^{4 k} \equiv 6^{k} \equiv 6^{★} . . . . v$ $i i i \times i v : 8^{7} \equiv 2 . . . v i$ $v \times v i : 8^{4 k + 7} \equiv 2$ $\begin{matrix} 8^{n + 4} \equiv 2 \end{matrix}$ $\begin{matrix} ^{★} 6^{k} \equiv 6 (m o d 10) \end{matrix}$
	Commented by mnjuly1970 last updated on 14/Dec/22

	$t h x a l o t s i r R a s h e e d$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum