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

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Subject: It is required to find the least whole number, which, being
divided by...
From: henha...@gmail.com (henh...@gmail.com)
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by: henh...@gmail.com - Sat, 18 Jun 2022 19:03 UTC

[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.

Re: It is required to find the least whole number, which, being divided by...

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From: emurph...@zoho.com (Edward Murphy)
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Subject: Re: It is required to find the least whole number, which, being
divided by...
Date: Sun, 19 Jun 2022 17:28:04 -0700
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by: Edward Murphy - Mon, 20 Jun 2022 00:28 UTC

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.

Subject	Author
It is required to find the least whole number, which, being	henh...@gmail.com
Re: It is required to find the least whole number, which, being	Edward Murphy