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Uva 10179 – Irreducable Basic Fractions | Shipu's Blog
Problem Link Definition Euler function (sometimes denoted or ) - is the amount of numbers from up to prime to . In other words, the number of properties in the interval , the greatest common divisor of which a root of unity. The first few values ​​of this function ( A000010 in OEIS encyclopedia ): Properties The following three simple properties of the Euler - enough to learn how to calculate it for any number: If - prime, then . (This is obvious, since any number, except for the relatively easy with him.) If - simple - positive integer, then . (Because the number of not only relatively prime numbers of the form , which the pieces.) If and are relatively prime, then ("multiplicative" Euler function). (This follows from the Chinese Remainder Theorem . Consider an arbitrary number . denote and the remainders at and , respectively. then prime to if and only if the prime to and separately, or what is the same thing as a one- simply and relatively prime to . Applying the Chinese