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Old 2006-05-29, 16:46   #1
mfgoode
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Lightbulb Easy number theory.


A 3 digit number in the scale of 7 has its digits reversed when expressed in the scale of 9. Find the number in all three scales, 7 ,9 and 10.
Mally
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Old 2006-05-29, 17:03   #2
alpertron
 
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49k+7m+n = 81n+9m+k

48k-2m-80n = 0
24k-m-40n = 0

1<=k<=6
0<=m<=6
1<=n<=6

m must be multiple of gcd(24,40) = 8, so m=0

m = 0 -> 24k-40m = 0 -> k=5, n=3

So the number in base 7 is 503 (248 decimal), which is equal to 305 in base 9.

Last fiddled with by alpertron on 2006-05-29 at 17:04 Reason: Missing spoiler tags
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Old 2006-05-30, 09:46   #3
mfgoode
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Thumbs up Easy number theory.


Fine deduction Alpertron!
I thought the digit 8 coming in to the calculations would stump any one in forming the equations.
I must bear you in mind when I give my next problem and make it more challenging.
Mally
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