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

Asked by architsrivastava02 | 9th Sep, 2010, 04:07: PM

Expert Answer:

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

Answered by  | 16th Sep, 2010, 10:06: AM

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