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4
G 4
G 4
Source:
May 25, 2007
Putnam
absolute value
Irrational numbers
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be integers, not all zero and each of absolute value less than one million. Prove that
∣
a
+
b
2
+
c
3
∣
>
1
1
0
21
.
\left\vert a+b\sqrt{2}+c\sqrt{3}\right\vert > \frac{1}{10^{21}}.
a
+
b
2
+
c
3
>
1
0
21
1
.
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