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National and Regional Contests
South Africa Contests
South Africa National Olympiad
2010 South africa National Olympiad
1
1
Part of
2010 South africa National Olympiad
Problems
(1)
Sum of its digits plus the square of its units digit
Source: South African MO 2010 Q1
5/26/2012
For a positive integer
n
n
n
,
S
(
n
)
S(n)
S
(
n
)
denotes the sum of its digits and
U
(
n
)
U(n)
U
(
n
)
its unit digit. Determine all positive integers
n
n
n
with the property that
n
=
S
(
n
)
+
U
(
n
)
2
.
n = S(n) + U(n)^2.
n
=
S
(
n
)
+
U
(
n
)
2
.
number theory unsolved
number theory