So θ ≡ 0 mod 45, but θ ≢ 0 mod 90.

Wed, 06 May 2026 17:31:26 +0000

Understanding the Modular Condition: θ ≡ 0 mod 45, but θ ≢ 0 mod 90 When exploring modular arithmetic, one frequently encounters conditions that restrict integers into precise equivalence classes. A particularly interesting case arises with the condition: > θ ≡ 0 mod 45, but θ ≢ 0 mod 90. This means that θ is a multiple of 45, but it is not a multiple of 90. Such a condition defines a specific subset of integers with unique properties, useful in number theory, cryptography, and algorithmic design. In this article, we’ll unpack what this condition means, explore examples, and explore its mathematical implications.