Finding the Remainder.
Number Theory
Level
1
Find the remainder when
is divided by 7 for any value of ?
The answer is 1.
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1 solution
Since, gcd(10,7)=1, we can use fermat's little theorem on 10 and 7. so, by fermat's little theorem, we have- 10^(7-1)=1(mod 7) =>10^6=1(mod 7) =>(10^6)^n=1^n=1(mod 7) =>10^(6n)=1(mod 7) Hence, proved. Note:- here '=' sign means congruence.