Question 403728: Hi am slightly stuck on this question on number theory. I have solved it up to a point but don’t know how to get the values of (a, b, c)
Question. If abc + abc = cba in the scale of five (when abc means 5²a + 5b + c) find the values of a, b, c
Solution so far
Since the numbers are in the base 5 abc+abc=cba means
(25a+5b+c) + (25a+5b+c) = 25c+5b+a
Solving gives: 50a+10b+2c = 25c+5b+a
49a+5b = 23c
This is where I am stuck how do we find the values of a,b,c do we SOLVE or do we use trial and error and is there another method for solving the equation, which would give us the same answer.
The answer for a, b, c is given as 1, 4, 3
Ps the numbers are in the scale of five.
Thanks moses.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If abc + abc = cba in the scale of five (when abc means 5²a + 5b + c) find the values of a, b, c
Solution so far
Since the numbers are in the base 5 abc+abc=cba means
(25a+5b+c) + (25a+5b+c) = 25c+5b+a
Solving gives: 50a+10b+2c = 25c+5b+a
49a+5b = 23c
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If you do trial and error, it wouldn't take long.
c has to be more than 2 since the LHS has a minimum value of 54 (49+5)
If you start at c = 3, the solution is simple.
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You can google Diophantie equations, too, about integer solutions.
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