Question 26
Adding 1 to the product of four consecutive positive integers always results in a perfect square. The first 2017 such square numbers can be found:
1 × 2 × 3 × 4 + 1 = 25 = 5²
2 × 3 × 4 × 5 + 1 = 121 = 11²
3 × 4 × 5 × 6 + 1 = 361 = 19²
⋮
2017 × 2018 × 2019 × 2020 + 1 = 16600254584281 = 4074341²
In the list of 2017 numbers 5, 11, 19, …, 4074341 whose squares are found in this way, how many have last digit equal to 1?
1 × 2 × 3 × 4 + 1 = 25 = 5²
2 × 3 × 4 × 5 + 1 = 121 = 11²
3 × 4 × 5 × 6 + 1 = 361 = 19²
⋮
2017 × 2018 × 2019 × 2020 + 1 = 16600254584281 = 4074341²
In the list of 2017 numbers 5, 11, 19, …, 4074341 whose squares are found in this way, how many have last digit equal to 1?