Suppose 2a≡2b(mod101). Is a≡b(mod100) always true?
The first thing that came in my mind was Fermat's Little Theorem. WLOG a≥b. Since (101,2)=1, dividing both sides by 2b gives 2a−b≡1(mod101)
Also, 2100≡1(mod101)
by Fermat's Little Theorem.
How should I continue?
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