On some congruences for primality
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In this paper we consider some congruences on arithmetical functions, sat-ised by the prime numbers. For example, we study the congruencesn (n) 2(mod '(n)),n' (n) 2 (mod (n)),(n)d(n) 2 0 (mod n), where'(n),(n),d(n) denote Euler's totient, Dedekind's function, and the number ofdivisors ofn, respectively. Two duals of the Lehmer congruencen 1 0(mod '(n)) are also introduced.
Abstract
In this paper we consider some congruences on arithmetical functions, sat-ised by the prime numbers. For example, we study the congruencesn (n) 2(mod '(n)),n' (n) 2 (mod (n)),(n)d(n) 2 0 (mod n), where'(n),(n),d(n) denote Euler's totient, Dedekind's function, and the number ofdivisors ofn, respectively. Two duals of the Lehmer congruencen 1 0(mod '(n)) are also introduced.
참고문헌 (7)
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- J. S¶andor, "On some diophantine equations for particular arithmetic functions", Seminarul de t. structurilor, (53) (1989), Univ. Timi»soara.
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- J. S¶andor, "Handbook of number theory II" (2005), Springer Verlag
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