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including olympiad champions, researchers, and professionals.

examples, and problems from the community.

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Solve integer equations, determine remainders of powers, and much more with the power of Modular Arithmetic.

Find the remainder when \(3^{247}\) is divided by \(17\).

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by
**
Mardokay Mosazghi**

\[\Large 1+\dfrac{1}{2} + \dfrac{1}{3} + \ldots + \dfrac{1}{23} = \dfrac{a}{23!}\]

Find the remainder when \(a\) is divided by 13.

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**
Surya Prakash**

Find the last three digits of the number

\[ 3 \times 7 \times 11 \times 15 \times \cdots \times 2003. \]

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by
**
Varun Vijay**

Find the smallest positive integer \(N\) such that \( 13^N \equiv 1 \pmod{2013}\).

**Details and assumptions**

You may choose to refer to Modulo Arithmetic notation.

0 is not a positive integer.

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by
**
Calvin Lin**

Find the **GCD** of \((19! + 19, 20! + 19).\)

**Details and Assumptions:**

- Here
**GCD**denotes greatest common divisor.

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by
**
Anuj Shikarkhane**

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