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Let a, b, c, d be four integers such that a + b
+c+d=4m + 1 where is a positive integer.
Which one of the following is necessarily true?
(1) The minimum possible value of a^2 + b^2+
c^2+d^2 is 4m^2-2m +1
(2) The minimum possible value of a^2 + b^2 +
c^2+d^2 is 4m^2 +2m +1
(3) The maximum possible value of a^2 + b^2 +
C^2+d^2 is 4m^2 - 2m + 1
(4) The maximum possible value of a^2 + b^2 +
c^2 + d^2 is 4m^2 + 2m + 1

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