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Composite Sum Satisfaction (Posted on 2014-11-11) Difficulty: 3 of 5
Determine the largest even positive integer that cannot be written as the sum of two odd composite positive integers.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution solution | Comment 2 of 4 |


38 is the answer


For an even integer over  38:


If it's 0 mod 3, then it equals 3*3+ an odd multiple of 3;


If it's 1 mod 3, then it equals 5*5 + an odd multiple of 3;


If it's  2 mod f 3, then it's 35 plus an odd multiple of 3.

In all those cases  there exist two composite addends.

Therefore the largest possible one is 38.


38=1+37=3+35=5+33=7+31=9+29=11+27=13+25=
=15+23=17+21=19+19

In each of the above couples at least one number is a prime.



  Posted by Ady TZIDON on 2014-11-11 10:50:36
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