Solve, given all unknowns are non-zero integers

Solve, given all unknowns are non-zero integers

The set has the property that the product of any two of them plus one is the square of a rational number.

………. ………. ……….

………. ……….

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are all perfect squares

Here we have

To find the smallest integer whose first **n** multiples all contain a 3

153×1, 153×2

1153×1, 1153×2, 1153×3

1183×1, 1183×2, 1183×3, 1183×4

3465×1, 3465×2, 3465×3, 3465×4, 3465×5

34566×1, 34566×2, 34566×3, 34566×4, 34566×5, 34566×6

53465×1, 53465×2, 53465×3, 53465×4, 53465×5, 53465×6, 53465×7

7673×1, 7673×2, 7673×3, 7673×4, 7673×5, 7673×6, 7673×7, 7673×8

Can you find an integer whose first **9** multiples all contain a 3?

What about the smallest integer whose first **10** multiples all contain a 3?

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Paul’s solutions:

first 9 multiples of 65913

first 9 multiples of 76923

first 10 multiples of 65913

first 10 multiples of 76923

first 11 multiples of 65913

first 11 multiples of 76923

first 12 multiples of 76923

first 13 multiples of 232767

first 13 multiples of 257673

first 14 multiples of 232767

first 14 multiples of 257673

first 15 multiples of 232767

first 15 multiples of 257673

first 16 multiples of 232767

first 17 multiples of 232767

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first 18 multiples of 7692391

Can you find an integer whose first **19** multiples all contain a 3?

Can you find an integer whose first **20** multiples all contain a 3?

first 21 multiples of 2307767

first 22 multiples of 3076923

first 23 multiples of 6923313

The set has the property that the product of any two of them plus one is the square of a rational number.

………. ………. ……….

………. ……….

……….

are all perfect squares

where

The set has the property that the product of any two of them plus one is the square of a rational number.

where

The set has the property that the product of any two of them plus one is the square of a rational number.

where

the next solutions are:

Find the next set.

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Or

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Or

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