MathDB

St.Peterburg, P7 Grade 9, 2013

Source:

April 27, 2014

modular arithmeticnumber theory proposednumber theory

Problem Statement

Given is a natural number

a

with

54

digits, each digit equal to

0

1

. Prove the remainder of

a

when divide by

33\cdot 34\cdots 39

is larger than

100000

. (It's mean:

a \equiv r \pmod{33\cdot 34\cdots 39 }

with

0<r<33\cdot 34\cdots 39

then prove that

r>100000

) M. Antipov