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1) What is the smallest positive integer n such that the rightmost three digits of n! and (n+1)! are the same?

 

2)  \(N=1991\cdot1993\cdot1995\cdot1997\cdot1999. \) What is the sum of the hundreds, tens and units digits of N?

 

3) What is the remainder when \(2+4+6+\cdots+100 \) is divided by 7?

 Oct 24, 2020
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1 - n = 10! =3,628,800  and (10+1)! = 11! =39,916,800

 

2 - N=1991*1993*1995*1997*1999 = N = 31601836203377055. Sum = 0 + 5 + 5 = 10

 

3 - sumfor(n, 1, 50, 2*n) = 2550 mod 7 = 2 - the remainder

 Oct 24, 2020

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