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Cauchy's functional equation is the functional equation: (+) = + (). A function that solves this equation is called an additive function.Over the rational numbers, it can be shown using elementary algebra that there is a single family of solutions, namely : for any rational constant .
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1) = 1 and = () whenever a and b are coprime.. An arithmetic function f(n) is said to be completely multiplicative (or totally multiplicative) if f(1) = 1 and f(ab) = f(a)f(b) holds for all positive integers a and b, even when they are not coprime.
It can penetrate a 6 mm (0.2 in) thick St3 steel plate at 300 m (328 yd) and 6Zh85T body armour at 30 m (33 yd). [citation needed] The 7N23 armour-piercing bullet, introduced in 2002, has a 3.6 g (55.6 gr) sharp-pointed steel penetrator made of steel U12A and retains the soft lead plug in the nose for jacket discarding. The bullet has a black tip.