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 Remainders (Posted on 2006-04-15)
A={the set of all positive integers leaving a remainder of 4 when divided by 45}
B={the set of all positive integers leaving a remainder of 45 when divided by 454}
C={the set of all positive integers leaving a remainder of 454 when divided by 4545}
D={the set of all positive integers leaving a remainder of 4545 when divided by 45454}

Find the smallest number in the intersection of
1)Sets A and B;
2)Sets A and B and C;
3)Sets A and B and C and D.

 See The Solution Submitted by Jer Rating: 3.5000 (2 votes)

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 computer solution | Comment 2 of 3 |

In UBASIC:

list
10   N=45+4
15   Incr=45
20   while 1=1
30   N=N+Incr
40   if N@454=45 then
50   :if Did=0 then print N;"B":Did=1:Incr=lcm(45,454):endif
60   :if N@4545=454 then
70   :if Did2=0 then print N;"BC":Did2=1:Incr=lcm(45,454,4545):endif
80   :if N@45454=4545 then
90   :print N;"BCD":end
100   :endif:endif
110   wend
OK
run
499 B
41359 BC
35641667749 BCD
OK

 Posted by Charlie on 2006-04-15 18:39:50

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