When 25∧25 is divided by 26 , the remainder is
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This is the same as asking: what is 25^25 mod 26.
You can use modulo algebra property:
(A*B) mod C = (A mod C)*(B mod C).
Hence you problem might be split into:
25*25^24 mod 26 = (25 mod 26)*((25^2)^12 mod 26) =
= 25*(625^12 mod 26) = 25*(625 mod 26)^12 = 25*1^12 =
= 25.
You can use modulo algebra property:
(A*B) mod C = (A mod C)*(B mod C).
Hence you problem might be split into:
25*25^24 mod 26 = (25 mod 26)*((25^2)^12 mod 26) =
= 25*(625^12 mod 26) = 25*(625 mod 26)^12 = 25*1^12 =
= 25.
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