MATH 115B PROBLEM SET VI
JUNE 5, 2007
(1) Show that there are infinitely many even integers
n
with the property that both
n
+ 1
and (
n/
2) + 1 are perfect squares. Exhibit two such integers.
(2) Find the fundamental solutions of the following equations:
(i)
x
2

29
y
2
= 1;
(ii)
x
2

41
y
2
= 1.
(3)(a) Prove that whenever the equation
x
2

dy
2
=
c
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 Fall '09
 Equations, Integers, Solubility, Prime number, equation x2

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