Solution: We are asked to count how many of the first 100 positive integers satisfy the congruence:

Wed, 06 May 2026 00:36:58 +0000

Understanding and Solving: Counting How Many of the First 100 Positive Integers Satisfy a Given Congruence When it comes to number theory in mathematics, congruences play a vital role—especially in problems involving modular arithmetic. A common challenge often presented is:
How many of the first 100 positive integers satisfy a particular congruence condition? While the exact congruence isn’t specified, this article explores a general solution approach using modular arithmetic, walk through practical examples, and provides methods to efficiently count solutions within a finite range—such as the first 100 positive integers. ---