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its impossible
This is impossible with positive integers. However, four numbers separated by a difference of 1 with a sum of -92 are: -21.5 -22.5 -23.5 -24.5
Integers by definition do not have any decimals, so that is impossible.
Most numbers ARE rational. For instance all the integers and most real numbers are rational numbers. To be an irrational number a real number must be impossible to express as a ratio of integers.
This is impossible, in mathematical terms. If you take two consecutive integers, then one of the integers must be odd and the other must be even. When you add an odd number to an even number, the result is always an odd number. Here, you said two consecutive integers add up to 26, which is an even number. Therefore, the answer is "No real solutions."