Coprime
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COPRIMALITY CRITERION OF SMARANDACHE
Let a and b be strictly positive coprime integers. F(b)+1 a
Then:
F(a)+1 +
b
is congruent to
a + b ( mod ab ),
where F is Euler's totient function. References: [1] Dumitrescu, C., Seleacu, V., "Some notions and questions in number theory", Erhus Univ. Press, Glendale, 1994, Section #118 ("Smarandache Criterion of Coprimality"). [2] Smarandache, Florentin, "Collected Problems of Mathematics", University of Kishinev Press, Kishinev, 1997, Problem 37, p. 26.
Let a and b be strictly positive coprime integers. F(b)+1 a
Then:
F(a)+1 +
b
is congruent to
a + b ( mod ab ),
where F is Euler's totient function. References: [1] Dumitrescu, C., Seleacu, V., "Some notions and questions in number theory", Erhus Univ. Press, Glendale, 1994, Section #118 ("Smarandache Criterion of Coprimality"). [2] Smarandache, Florentin, "Collected Problems of Mathematics", University of Kishinev Press, Kishinev, 1997, Problem 37, p. 26.
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