perplexus.info :: Numbers : Using its own digits

Using its own digits (Posted on 2018-05-31)

a.What two-digit number equals the product of units' digit by the factorial of tens' digit?
b. What if a non-decimal system (base below ten) were allowed?

See The Solution Submitted by Ady TZIDON

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beyond base 10, analytical solution

| Comment 2 of 9 |

let the two digit number by xy and the base b.

Then we require

bx+y=y*x!

solving for b we get

b=y(x!-1)/x

since gcd(x,x!-1) then we need x to divide y

so for any two digits x,y where x divides y, selecting a base
b=y(x!-1)/x would seem to make this work

Posted by Daniel on 2018-05-31 23:55:17

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