What is the remainder 9^ 113*7^110 is divided by 31?
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9 ^ 113 × 7 ^ 110
9^113
113 / 4 = 1 ( remainder )
= 9^1 ----(1)
7^ 110
110 / 4 = 2 ( remainder )
7 ^2 .....(2)
multiply (1) and (2)
9 × 7 ^2 = 441
441 / 4 = 1 ( remainder)
Remainder = ( 31 + 1 )/ 2
= 32 / 2 = 16 .
hence , remainder = 16
9^113
113 / 4 = 1 ( remainder )
= 9^1 ----(1)
7^ 110
110 / 4 = 2 ( remainder )
7 ^2 .....(2)
multiply (1) and (2)
9 × 7 ^2 = 441
441 / 4 = 1 ( remainder)
Remainder = ( 31 + 1 )/ 2
= 32 / 2 = 16 .
hence , remainder = 16
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