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Rioplatense Mathematical Olympiad, Level 3
2000 Rioplatense Mathematical Olympiad, Level 3
1
1
Part of
2000 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
b^2+(b +1)^2+...+(b + a)^2 -3 mutiple of 5, a+b = odd, digit of units of (a+b)?
Source: Rioplatense Olympiad 2000 level 3 P1
9/6/2018
Let
a
a
a
and
b
b
b
be positive integers such that the number
b
2
+
(
b
+
1
)
2
+
.
.
.
+
(
b
+
a
)
2
ā
3
b^2 + (b +1)^2 +...+ (b + a)^2-3
b
2
+
(
b
+
1
)
2
+
...
+
(
b
+
a
)
2
ā
3
is multiple of
5
5
5
and
a
+
b
a + b
a
+
b
is odd. Calculate the digit of the units of the number
a
+
b
a + b
a
+
b
written in decimal notation.
number theory
odd
multiple
Last digit