The integer 9 can be written as a sum of two consecutive integers: 9 \equal{} 4\plus{}5. Moreover, it can be written as a sum of (more than one) consecutive positive integers in exactly two ways: 9 \equal{} 4\plus{}5 \equal{} 2\plus{}3\plus{}4. Is there an integer that can be written as a sum of 1990 consecutive integers and that can be written as a sum of (more than one) consecutive positive integers in exactly 1990 ways? number theoryAdditive combinatoricsAdditive Number TheorycountingIMO Shortlist