Unique solutions (requiring an odd power) to Pillai's equation for n <= 1000 Perfect powers examined up to 2^63-1 n for which there is a unique solution requiring an odd power: 1, 2, 10, 30, 38, 46, 122, 126, 138, 142, 146, 150, 154, 166, 170, 190, 194, 214, 222, 234, 270, 282, 298, 318, 338, 342, 354, 370, 382, 386, 406, 486, 490, 498, 502, 518, 546, 550, 566, 574, 582, 586, 594, 638, 666, 678, 686, 694, 710, 726, 730, 734, 746, 774, 806, 814, 818, 834, 838, 878, 894, 906, 930, 934, 938, 962, 970, 974, 982 Total number of solutions: 69 Solutions for each n: 1 = 3^2 - 2^3 2 = 3^3 - 5^2 10 = 13^3 - 3^7 30 = 83^2 - 19^3 38 = 37^2 - 11^3 46 = 17^2 - 3^5 122 = 3^5 - 11^2 126 = 15^3 - 57^2 138 = 173^2 - 31^3 142 = 13^2 - 3^3 146 = 195^3 - 2723^2 150 = 175^3 - 2315^2 154 = 111^2 - 23^3 166 = 7^5 - 129^2 170 = 59^3 - 453^2 190 = 39^2 - 11^3 194 = 3^5 - 7^2 214 = 49^2 - 3^7 222 = 7^3 - 11^2 234 = 3^5 - 3^2 270 = 39^3 - 9^5 282 = 25^2 - 7^3 298 = 19^3 - 81^2 318 = 7^3 - 5^2 338 = 3^7 - 43^2 342 = 7^3 - 1^2 354 = 131^2 - 7^5 370 = 11^3 - 31^2 382 = 25^2 - 3^5 386 = 9^3 - 7^3 406 = 1107^2 - 107^3 486 = 9^3 - 3^5 490 = 11^3 - 29^2 498 = 29^2 - 7^3 502 = 23^2 - 3^3 518 = 43^2 - 11^3 546 = 43^3 - 281^2 550 = 31^3 - 171^2 566 = 15^3 - 53^2 574 = 365^2 - 51^3 582 = 283^2 - 43^3 586 = 115^3 - 1233^2 594 = 63^2 - 15^3 638 = 549^2 - 67^3 666 = 3^7 - 39^2 678 = 7^5 - 127^2 686 = 2395^2 - 179^3 694 = 45^2 - 11^3 710 = 87^2 - 19^3 726 = 55^3 - 407^2 730 = 3511^2 - 231^3 734 = 15^5 - 871^2 746 = 33^2 - 7^3 774 = 15^3 - 51^2 806 = 209^2 - 35^3 814 = 29^2 - 3^3 818 = 3^7 - 37^2 834 = 175^2 - 31^3 838 = 55^2 - 3^7 878 = 47^2 - 11^3 894 = 7^7 - 907^2 906 = 409^2 - 55^3 930 = 19^3 - 77^2 934 = 31^2 - 3^3 938 = 5^5 - 3^7 962 = 3^7 - 35^2 970 = 11^3 - 19^2 974 = 15^3 - 49^2 982 = 35^2 - 3^5