• #### It is required to find the least whole number, which, being divided by.

From henhanna@gmail.com@21:1/5 to All on Sat Jun 18 12:03:48 2022
[A] It is required to find the least whole number, which,
being divided by 7, 8, and 9, respectively, shall leave the remainders 6, 7, and 8.

[B] It is required to find the least whole number, which,
being divided by 7, 8, and 9, respectively, shall leave the remainders 5, 7, and 8.

[C] It is required to find the least whole number, which,
being divided by each of the nine digits, 1, 2, 3, 4, 5, 6, 7,
8, 9, shall leave no remainders.

pls wait 1 week (or almost that) before posting answer(s) or hints.

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• From Edward Murphy@21:1/5 to henh...@gmail.com on Sun Jun 19 17:28:04 2022
On 6/18/2022 12:03 PM, henh...@gmail.com wrote:

[A] It is required to find the least whole number, which,
being divided by 7, 8, and 9, respectively, shall leave the remainders 6, 7, and 8.

[B] It is required to find the least whole number, which,
being divided by 7, 8, and 9, respectively, shall leave the remainders 5, 7, and 8.

[C] It is required to find the least whole number, which,
being divided by each of the nine digits, 1, 2, 3, 4, 5, 6, 7, 8, 9, shall leave no remainders.

pls wait 1 week (or almost that) before posting answer(s) or hints.

[N] Vs guvf ahzore vf k, gura k+1 vf qvivfvoyr ol 7, 8, naq 9. Nf vg'f
terngre guna mreb, gur fznyyrfg inyhr vf 7*8*9 = 504, fb gur qrfverq
ahzore vf 503.

[O] Svefg svaq k fhpu gung k = 7 (zbq 8) naq k = 8 (zbq 9). Ol
ernfbavat fvzvyne gb [N], k zhfg or bar yrff guna n zhygvcyr bs 72,
fb vafcrpg gubfr hagvy jr svaq gur qrfverq erzvaqre zbq 7:
71 = 1 (zbq 7)
143 = 3 (zbq 7)
215 = 5 (zbq 7)
fb gur qrfverq ahzore vf 215.

[P] Mreb. Yrnfg cbfvgvir jubyr ahzore vf 2^3 * 3^2 * 5 * 7 = 2520.

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