Question

Let t= 20389208 mod 4 and M= t+25. Find the following,

a. (i) 2^M mod 7; (ii) 10^M mod 7; (iii) 3^M mod 7

b. 20389208 mod m for m= 2,3,5,9 and 11

c. 123456789987654321 mod m for m= 2,3,4,5,9 and 11

Answer 1

mod-modulo operator This operator give remaider when we perform division

t=0 M=t+25 which is M=25

a.(i)2^M mod 7

=2^25 mod 7

=33554432 mod 7

=2

(ii)10^M mod 7

=10^25 mod 7

= 1.0000e+25 mod 7

=1

(iii)3^M mod 7

=3^25 mod 7

=8.4729e+11 mod 7

=1

b) 20389208 mod 2

=0

20389208 mod 3

=2

20389208 mod 4

=0

20389208 mod 5

=3

20389208 mod 9

=5

20389208 mod 11

=4

(iii) 123456789987654321 mod 2

=1

123456789987654321 mod 3

=0

123456789987654321 mod 4

=1

123456789987654321 mod 5

=1

123456789987654321 mod 9

=0

123456789987654321 mod 11

=0