Number Theory
# Modular Arithmetic Operations

What is the smallest (positive) integer \(N\), such that when \(N\) is rotated, we obtain \( \frac{2}{3} N \)?

Find the remainder when \(6^{98}+8^{98}\) is divided by 98.

Find the smallest positive integer \(k\) such that \(1^2+2^2+3^2+\ldots+k^2\) is a multiple of 200.

\[{a^x \equiv a-2 \pmod{{\small(a-1)}}}\]

If \(a\) and \(x\) are positive integers greater than 2, what is the value of \(a?\)

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