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Special feature (Posted on 2018-07-29) Difficulty: 3 of 5
What is the biggest even number N that can't be written as a sum of odd composite numbers?

Bonus: Find another feature unique to N.

  Submitted by Ady TZIDON    
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Solution: (Hide)
Consider the three odd composites 9,25,35. These are, respectively, 0,1,2(mod3).
Thus, if n is an even number, one of n−9,n−25,n−35 is an odd composite divisible by 3 (well, supposing it is >3 at least).
So 35+3=38 is the largest even number that qualifies!

Some special features:
38 is the last Roman numeral when written lexicographically (XXXVIII).
38 is the largest known even number which can be represented as sum of two distinct primes in only one way: 38 = 31 + 7
38 is the sum of the squares of the first three primes: 38 = 2^2 + 3^2 + 5^2
38 is magic hexagon's smallest integer constant

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/TipsNo SubjectAdy TZIDON2018-08-06 21:08:58
Some Thoughtsre(3): computer solution and tidbits from a referenceDej Mar2018-07-31 10:16:10
re(2): computer solution and tidbits from a referenceCharlie2018-07-30 12:21:41
Some Thoughtsre: computer solution and tidbits from a referenceDej Mar2018-07-30 03:08:53
Solutioncomputer solution and tidbits from a referenceCharlie2018-07-29 13:06:40
SolutionJer2018-07-29 11:13:33
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