Geodesic
On a Conjecture of Graham Concerning a Sequence of Integers
Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 285-287

Voir la notice de l'article provenant de la source Cambridge University Press

Let 0<a1<...<an be integers and (a, b) denotes the greatest common divisor of a, b. R. L. Graham [1] has conjectured that for some i and j. In a recent paper Weinstein [2] has improved Winterle's result [3] and has proven the following interesting theorem:If A is the sequence a1< ... <an where ak = P, a prime for some k and , then . 
Chein, E. Z. On a Conjecture of Graham Concerning a Sequence of Integers. Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 285-287. doi: 10.4153/CMB-1978-050-7
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[1] 1. Graham, R. L., Unsolved problem 5749, Amer. Math. Monthly 77 (1970), 775. Google Scholar

[2] 2. Weinstein, G. On a conjecture of Graham concerning greatest common divisors proceedings Amer. Math. Soc. 63 (1977), 33-38. Google Scholar

[3] 3. Winterle, Riko, A problem of R. L. Graham in combinatorial number theory, Proc. Louisiana Conf. on Combinatorics, Graph Theory and Computing (Louisiana State Univ, Baton Rouge, La., 1970, pp. 357-361. MR 42 #3051. Google Scholar

[4] 4. Vélez, W. Y., Some remarks on a number theoretic problem of Graham, Acta. Arith. 32 (1977), no. 3, 233-238. Google Scholar

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