1. The sum of 13 different positive integers is 100. Find the maximum and minimum value of the number of even numbers among them.
2. Write down several positive integers such that their sum is 17. Find the maximum value of their product.
3. Find the greatest prime number which cannot be expressed as the sum of 3 composite numbers.
Problems about Number Theory
2009-11-15 8:35 pm
回答 (1)
2009-11-15 9:22 pm
✔ 最佳答案
(1) 2+4+6+8+10+12+22+1+3+5+7+9+11=1001+3+5+7+9+11+13+15+17+19=100
Max=7,Min=0
(2) 1+16=17,2+15=17,3+3+3+3+3+2=17 which has the max. value 486
(3) every integer n>=12 is the sum of two composite numbers. So just think 2,3,5,7,11 and the answer is 11
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