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1993 USAMO
1
Which is larger
Which is larger
Source: USAMO 1993
October 27, 2005
function
algebra unsolved
algebra
USAMO
1993
Problem Statement
For each integer
n
≥
2
,
\, n \geq 2, \,
n
≥
2
,
determine, with proof, which of the two positive real numbers
a
\, a \,
a
and
b
\, b \,
b
satisfying
a
n
=
a
+
1
,
b
2
n
=
b
+
3
a
a^n = a + 1, \hspace{.3in} b^{2n} = b + 3a
a
n
=
a
+
1
,
b
2
n
=
b
+
3
a
is larger.
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