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New Zealand Contests
NZMOC Camp Selection Problems
2017 NZMOC Camp Selection Problems
7
7
Part of
2017 NZMOC Camp Selection Problems
Problems
(1)
ac + bd is composite if a^4 + b^4 = c^4 + d^4 = e^5
Source: New Zealand NZMOC Camp Selection Problems 2017 p7
9/19/2021
Let
a
,
b
,
c
,
d
,
e
a, b, c, d, e
a
,
b
,
c
,
d
,
e
be distinct positive integers such that
a
4
+
b
4
=
c
4
+
d
4
=
e
5
.
a^4 + b^4 = c^4 + d^4 = e^5.
a
4
+
b
4
=
c
4
+
d
4
=
e
5
.
Show that
a
c
+
b
d
ac + bd
a
c
+
b
d
is composite.
composition
number theory