Find all pairs (a, b) of positive integers that satisfy ab2 = ba.
2007-12-21 15:33:00 · 3 answers · asked by Anonymous in Education & Reference ➔ Homework Help
Find all pairs (a, b) of positive integers that satisfy (ab)^2 = ba.
2007-12-22 13:44:59 · update #1
Find all pairs (a, b) of positive integers that satisfy a^b^2 = ba.
Or
a [to the power of] b [to the power of] 2 = b [multiplied by] a
2007-12-23 12:52:32 · update #2
Actually, if by ab2 you mean a(b^2), then the answer to your question is (a, 1) where a is any positive number. b can't be 0 because 0 is neither positive nor negative.
If by ab2 you mean (ab)^2, then the answer is (a, 1/a) where a is any positive number.
But this seems like a strange question, especially since the order of a and b are switched on the right side of the equality, so you might want to check that you're reading it correctly...
2007-12-21 15:52:09 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Assuming you mean ab^2 = ba, then it is impossible to list all pairs.
ab^2=ba
b^2=b
That means A can be ANY number. (in your case, any positive number). B can only be zero or 1.
2007-12-21 23:37:27 · answer #2 · answered by tkquestion 7 · 1⤊ 0⤋
none
2007-12-21 23:38:04 · answer #3 · answered by spirit dummy 5 · 0⤊ 0⤋