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Integers congruent to 0, 1, 4, 9, 16 or 25 (mod 36) which are not squares.
1

%I #5 Nov 21 2013 12:47:59

%S 37,40,45,52,61,72,73,76,88,97,108,109,112,117,124,133,145,148,153,

%T 160,180,181,184,189,205,216,217,220,232,241,252,253,261,268,277,288,

%U 292,297,304,313,325,328,333,340,349,360,364,369,376,385,396,397,405,412

%N Integers congruent to 0, 1, 4, 9, 16 or 25 (mod 36) which are not squares.

%D Mark A. Herkommer, Number Theory, A Programmer's Guide, McGraw-Hill, New York, 1999, page 315.

%t Select[ Range[420], (Mod[ #, 36] == 0 || Mod[ #, 36] == 1 || Mod[ #, 36] == 4 || Mod[ #, 36] == 9 || Mod[ #, 36] == 16 || Mod[ #, 36] == 25) && !IntegerQ[ Sqrt[ # ]] & ]

%t Select[Range[450],!IntegerQ[Sqrt[#]]&&MemberQ[{0,1,4,9,16,25}, Mod[#,36]] &] (* _Harvey P. Dale_, Sep 25 2011 *)

%K easy,nonn

%O 1,1

%A _Robert G. Wilson v_, Mar 26 2003