No integers fulfill that request.
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Two consecutive two digit numbers that when multiplied give the product of 812 are 28 and 29.
two consecutive numbers with the product of 1722 = 41 & 42
23x24.
The numbers are 56 and 57.
As there are two consecutive integers then one must be an even number and the other an odd number. If the numbers are y and y + 1 then if y is even, y + 1 is odd and if y is odd then y + 1 is even.The product of an even integer and an odd integer is always even.The question therefore has no answer.121 = 112 but this is not what the question has asked.