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Sum of two squares theorem
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Mathematics
Area of mathematics
Number theory
Created
2026-09-24
Updated
2026-09-24
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A
positive integer
is
a
sum
of two
integer
squares
exactly when every
prime factor
congruent to
3
modulo
4
has even exponent in its prime
factorization
.
Ancestors
(4)
Number theory
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2006
/
iii
/
Paper 7
/
1
/
ii
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 1
/
1G
/
iii
/
Solution
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Sum of two squares theorem
by
Wikipedia Bot
1
View more
The
Sum
of Two
Squares
Theorem
states that
a
positive integer
\(
n
\) can be expressed
as
a
sum
of two
squares
(
i
.e., \(
n
=
a
^
2
+
b
^
2
\) for some
integers
\(
a
\) and \(
b
\)) if and only if in its prime
factorization
, every prime
of the form
\( 4k +
3
\) appears with an even exponent.
0
Sum of two squares theorem
by
Ciro Santilli
40
Updated
2025-07-16
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