The mystery of Factorials!!!!!!!
Number Theory
Level
2
(1!)^2 + (2!)^2 +(3!)^2.................(10000000000000000000000000!)^2 is when divided by (20)^2 then what is the remainder????????????
The answer is 217.
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1 solution
The remainder of the given expression is the remainder of sum of squares of first 4 numbers when divided by 400(square of 20) as all other terms after the fourth term is divisible by 400 i.e, 5! = 120 which is divisible by 20. So the remainder is the remainder of sum of squares of first 4 numbers divided by 400. That is: 1 + 4 + 36 + 576 = 617/400. So the remainder is 217.