MHB Uncovering Patterns in Questions

Thread starter SumitKumar
Start date Oct 3, 2020
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The discussion focuses on identifying patterns in the remainders of powers of two when divided by seven, specifically noting that the remainder is influenced by the exponent's division by three. Participants suggest analyzing the remainders of triangular numbers, represented as k(k+1)/2, when divided by three to uncover further patterns. The conversation emphasizes the importance of modular arithmetic in understanding these relationships. Ultimately, the goal is to establish a clear pattern that can be applied to similar mathematical problems. Understanding these patterns can enhance problem-solving skills in number theory.

Oct 3, 2020

SumitKumar

Please help me to find pattern in this question

Last edited by a moderator: Oct 3, 2020

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Oct 3, 2020

Opalg

Gold Member

MHB

Hi SumitKumar, and welcome to MHB!

The remainder when $2^n$ is divided by $7$ depends on the remainder when the exponent $n$ is divided by $3$. So you need to work out the pattern of remainders when numbers of the form $\dfrac{k(k+1)}2$ are divided by $3$.

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