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In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
Congruence modulo m is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations of addition, subtraction, and multiplication. Congruence modulo m is denoted a ≡ b (mod m). The parentheses mean that (mod m) applies to the entire equation, not just to the right-hand side (here, b).
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
A group of mod developers may join to form a "mod team". Doom (1993) was the first game to have a large modding community. [ 6 ] In exchange for the technical foundation to mod, id Software insisted that mods should only work with the retail version of the game (not the demo), which was respected by the modders and boosted Doom ' s sales.
However, the linear congruence 4x ≡ 6 (mod 10) has two solutions, namely, x = 4 and x = 9. The gcd(4, 10) = 2 and 2 does not divide 5, but does divide 6. Since gcd(3, 10) = 1, the linear congruence 3x ≡ 1 (mod 10) will have solutions, that is, modular multiplicative inverses of 3 modulo 10 will exist. In fact, 7 satisfies this congruence (i ...
On the other side, some companies actively encourage modding of their products. In cases such as TiVo and Google, there has been an informal agreement between the modders and the company in which the modders agree not to do anything that destroys the company's business model and the company agrees to support the modding community by providing technical specifications and information.
The United States Navy uses the terms "Mark" and "Mod" as a method to uniquely designate specific types and configurations of equipment that would otherwise lack military designations. The practice was adopted by the Naval Ordnance group in 1944, and was formalized in the MIL-STD-1661 MARK and MOD Nomenclature System [ 9 ] [ 10 ] in 1978.
A Minecraft mod is a mod that changes aspects of the sandbox game Minecraft. Minecraft mods can add additional content to the game, make tweaks to specific features, and optimize performance. Thousands of mods for the game have been created, with some mods even generating an income for their authors.