MathDB
Problems
Contests
National and Regional Contests
Italy Contests
ITAMO
1985 ITAMO
7
7
Part of
1985 ITAMO
Problems
(1)
Four integer variables
Source:
3/14/2006
Assume that
a
a
a
,
b
b
b
,
c
c
c
, and
d
d
d
are positive integers such that
a
5
=
b
4
a^5 = b^4
a
5
=
b
4
,
c
3
=
d
2
c^3 = d^2
c
3
=
d
2
, and
c
−
a
=
19
c - a = 19
c
−
a
=
19
. Determine
d
−
b
d - b
d
−
b
.