The conjecture that Euler's totient has no nontrivial prime congruences
The conjecture that Euler's totient has no nontrivial prime congruences
Let be prime, and let and be coprime integers. A Ramanujan-type congruence for Euler's totient function would have the form
for every . The totient congruence conjecture. There are no coprime integers for which this congruence holds for all . The claim expresses that Euler's totient function has no nontrivial Ramanujan-type congruences of this prime-modulus form; the source gives no resolution.
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Sources & referencesView supporting material
Primary source
William Craig and Mircea Merca, “On Ramanujan-type Congruences for Multiplicative Functions”, arXiv:2112.05649 (2022).
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