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7
ISI Problem 7 2018
ISI Problem 7 2018
Source:
May 13, 2018
number theory
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
are natural numbers such that
a
2
+
b
2
=
c
2
a^{2}+b^{2}=c^{2}
a
2
+
b
2
=
c
2
and
c
ā
b
=
1
c-b=1
c
ā
b
=
1
Prove that
(
i
)
(i)
(
i
)
a
a
a
is odd.
(
i
i
)
(ii)
(
ii
)
b
b
b
is divisible by
4
4
4
(
i
i
i
)
(iii)
(
iii
)
a
b
+
b
a
a^{b}+b^{a}
a
b
+
b
a
is divisible by
c
c
c
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