논문KCI 등재
ON THE EQUATION Φ(5m − 1) = 5ⁿ − 1
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Here, we show that the title equation has no positive integer solutions (m, n), where Φ is the Euler function.
Abstract
Here, we show that the title equation has no positive integer solutions (m, n), where Φ is the Euler function.
참고문헌 (13)
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- J. Cilleruelo, "Repunit Lehmer numbers", Proc. Edinb. Math. Soc, 54(1), pp.55~65 (2011)
- M. T. Damir, "Members of Lucas sequences whose Euler function is a power of 2", Fibonacci Quart, 52(1), pp.3~9 (2014)
- W. Ljunggren, "Some theorems on indeterminate equations of the form xn−1", x−1 = yq, 1943, pp.25, 17~20
- F. Luca, "Problem 10626", American Math. Monthly, 104, pp.871~ (1997)
- F. Luca, "Equations involving arithmetic functions of Fibonacci and Lucas numbers", Fi-bonacci Quart, 38(1), pp.49~55 (2000)
- F. Luca, "Euler indicators of binary recurrence sequences", Collect. Math, 53(2), pp.133~156 (2002)
- F. Luca, "On the Euler function of repdigits", Czechoslovak Math. J, 58(1), pp.51~59 (2008)
- F. Luca, "ϕ(F11) = 88", Divulg. Mat, 14(2), pp.101~106 (2006)
- F. Luca, "Equations with arithmetic functions of Pell numbers", Bull. Soc. Mat. Roumanie
- H. L. Montgomery, "The large sieve", Mathematika, 20, pp.119~134 (1973)
- J. B. Rosser, "Approximate formulas for some functions of prime numbers", Illinois J. Math, 6, pp.64~94 (1962)
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