There is no such number. A diameter can be any number that you like.
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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."
79
all verticals, horazontals and diagonals must add up to one common number
Every number you put in it must add up to 15 vertically, horizontally and diagonally.
No sum of any even numbers can add up to an odd number.