The solutions of $a^2 = b^d -3^c$ are in the form $(a, b, c, d) = ((46)27^t, (13)9^t, 6t+4, 3)$. This is done by using calculator. As per my calculator, I have checked some terms, which are satisfied the above cited equation. Now, my question is, is there any other forms of solutions? if there, how to examine?
Solutions of $a^2 = b^d -3^c$
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number-theory
diophantine-equations
elliptic-curves
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0$(1,2,1,2)$, $(1,4,1,1)$. – 2012-10-20
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0@GerryMyerson!you are really helping me always. But, I would like to learn the way to find solutions. Otherwise, my life long duty to upload only questions. please try to understand me and tell me, how to solve such equations mathematically. – 2012-10-20
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0The way I found those two solutions was, I saw that no matter what $a$ and $c$ are, I can always let $d=1$ and solve for $b$. So I took $a=c=1$, found $b^d=4$, which gave two solutions. – 2012-10-20
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0@GerryMyerson!this is somewhat good. – 2012-10-20