2006-05-29, 16:46 | #1 |
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts |
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 |
2006-05-29, 17:03 | #2 |
Aug 2002
Buenos Aires, Argentina
2×3^{2}×79 Posts |
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 |
2006-05-30, 09:46 | #3 |
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts |
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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