A number theory problem by Paul Ryan Longhas
The number above shows the concatenation of positive integers between 10 and 99 (inclusive), denote that value as .
What is the remainder when is divided by 99?
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2 solutions
Moderator note:
Great. For clarity, you should explain how you calculated .
N = 99 + 98 10^2 + 97 10^4 + ....... and so on. Notice that 99 mod 99 = 0 ;
98*10^2 mod 99 = 98 ;
97*10^4 mod 99 = 97 ; ...... and so on. Now , add them up ... remainder = 98 + 97 + ... + 10 =4905 ;
Divide 4905 by 99 to obtain 54 as remainder