Show that 2m1 is congruent to 1mod mSolutionIf two numbers a

Show that 2^(m-1) is congruent to 1(mod m).

Solution

If two numbers a and b leave the same remainder when divided by a third number m, then we say \"a is congruent to b modulo m\", and write a ? b ( mod m ).

here in the above problem

a=2^m-1

b=1

m=m

but according to the difination

remainder is not the same in both the case,so

2^(m-1) is not congruent to 1(mod m)

instead

\"2^(m-2) is congruent to 1(mod m)\" OR

2^(m)-2 is congruent to 1(mod m)