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Existence: There exists an integer denoted a −1 such that aa −1 ≡ 1 (mod m) if and only if a is coprime with m. This integer a −1 is called a modular multiplicative inverse of a modulo m. If a ≡ b (mod m) and a −1 exists, then a −1 ≡ b −1 (mod m) (compatibility with multiplicative inverse, and, if a = b, uniqueness modulo m).
convert an int into a double i2f 86 1000 0110 value → result convert an int into a float i2l 85 1000 0101 value → result convert an int into a long i2s 93 1001 0011 value → result convert an int into a short iadd 60 0110 0000 value1, value2 → result add two ints iaload 2e 0010 1110 arrayref, index → value load an int from an array iand
Within the context of integers, addition of one also plays a special role: for any integer a, the integer (a + 1) is the least integer greater than a, also known as the successor of a. [23] For instance, 3 is the successor of 2 and 7 is the successor of 6.
For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow . Carrying is emphasized in traditional mathematics , while curricula based on reform mathematics do not emphasize any specific method to find a correct answer.
class Foo {int bar (int a, int b) {return (a * 2) + b;} /* Overloaded method with the same name but different set of arguments */ int bar (int a) {return a * 2;}} A method is called using . notation on an object, or in the case of a static method, also on the name of a class.
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
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Typically, general-purpose microprocessors do not implement integer arithmetic operations using saturation arithmetic; instead, they use the easier-to-implement modular arithmetic, in which values exceeding the maximum value "wrap around" to the minimum value, like the hours on a clock passing from 12 to 1.