2 to the power 70 + 3 to the power 70 is divisible by which of these-a-13 b-32 -c-70 d-23

Dear Student

 

2⁷⁰+3⁷⁰  is divisible by 13.

Here i sthe solution

n	0	1	2	3	4	5	6
2^n mod 13	1	2	4	-5	3	6	-1
3^n mod 13	1	3	-4	1

'congmod( 2^70 = (2^(6*11+4)) = (2^(6*11))*(2^4), ((_1)^11 * (2^4)) = (_1 * 3) = (_3), 13 )
'congmod( 3^70 = (3^(3*23+1)) = ((3^3)^23)*3, (1^23) * 3 = (1*3) = (3, 13 )
So 'congmod( 2^70 + 3^70, (_3 + 3),13 = 0, 13

Hence the number is divisible by 13