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TOT 077 1984 Autumn S2 11 different remainders, div. by 100

Source:

August 24, 2019
number theorycombinatoricsremainderSumpermutations

Problem Statement

A set of numbers a1,a2,...,a100a_1, a_2 , . . . , a_{100} is obtained by rearranging the numbers 1,2,...,1001 , 2,..., 100 . Form the numbers b1=a1b_1=a_1 b2=a1+a2b_2= a_1 + a_2 b3=a1+a2+a3b_3=a_1 + a_2 + a_3 ... b100=a1+a2+...+a100b_{100}=a_1 + a_2 + ...+a_{100} Prove that among the remainders on dividing the numbers by 100,11100 , 11 of them are different .
( L . D . Kurlyandchik , Leningrad)
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