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.
………. ………. ……….
………. ……….
……….
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?
——————————————————————
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
——————————————————————
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.
………………….
………………….
………………….
……………………
……………………
………..
Or
……………………
……………………
………..
…………………………………………………………..
……………………………..
……………………………..
………………….
…………………………………………………………..
……………………….
……………………….
………….
Or
……………………….
……………………….
………….