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Consecutive Conclusion (Posted on 2014-09-30) Difficulty: 3 of 5
Determine the maximum possible value of N for which 311 is expressible as the sum of N consecutive positive integers.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Solution solution | Comment 1 of 8

Any odd composite number C can be represented by a product of 2 factors m*n,

such that the most closest factors are chosen.

Examples:  63=9*7. 625=125*5,  3^11=3^6*3^5  etc.

If m is e larger than  (or equal to) n, than the sequence of  2n-1  consecutive numbers , m in the middle, (n-1)/2 numbers before & (n-1)/2 numbers   will form an arithm. series adding up to m*n.

So:

 6+7+8+9+10+11+12= .5*(6+12)*7= 63;

123+124+125+126+127=.5*(123+127)*5= 625;

3^6-(3^5-1)/2+3^6-(3^5-1)/2+1+3^6-(3^5-1)/2+2+...3^6+3^6+,..3^6+(3^5-1)/2=.5*(3^6+3^6)*3^5= 3^11<p>

Answer: 3^5=243 numbers:

608,609,....729,730, ....850

 

 


  Posted by Ady TZIDON on 2014-09-30 14:27:54
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