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ISI Entrance Examination
2020 ISI Entrance Examination
7
7
Part of
2020 ISI Entrance Examination
Problems
(1)
ISI 2020 : Problem 7
Source: B.Stat & B.Math Entrance Exam 2020
9/20/2020
Consider a right-angled triangle with integer-valued sides
a
<
b
<
c
a<b<c
a
<
b
<
c
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are pairwise co-prime. Let
d
=
c
−
b
d=c-b
d
=
c
−
b
. Suppose
d
d
d
divides
a
a
a
. Then (a) Prove that
d
⩽
2
d\leqslant 2
d
⩽
2
. (b) Find all such triangles (i.e. all possible triplets
a
,
b
,
c
a,b,c
a
,
b
,
c
) with perimeter less than
100
100
100
.
isi
2020
number theory