1. compute the least non-negative residue of 4^n (mod 9) for n=1,2,3,4,5.... prove that 6*(4^n)=6 (mod...

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Basic Math

1. compute the least non-negative residue of 4^n (mod 9) forn=1,2,3,4,5.... prove that 6*(4^n)=6 (mod 9) for every n>0.
2. find nice tests for divisibility of numbers in base 34 byeach of 2,3,5,7,11,and 17.
3. in Z/15Z, find all solutions of : (i) [36]X=[78]. (ii)[42]X=[57] (iii) [25]X=[36]
4. in Z/26Z, find the inverse of [9], [11], [17], and [22]
4. write the set of solutions of x=5 mod24. x=17 (mod 18)
for all equation line, there are triple line.

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Ans 1 a Least Residue non negative number are 4 for n1 7 for n2 1 for n3 4 for n4 now terms will be repeat b The powers of 4 modulo 9 are 4 42 16 7 43 7 4 28 1 44 4 ie 4 7 1 4 7 1 4 7 1 But See Answer

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1. compute the least non-negative residue of 4^n (mod 9) for n=1,2,3,4,5.... prove that 6*(4^n)=6 (mod...

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