Take the elliptic curve y^2 = x^3 - 5 that has no rational solutions [1]. But it's easy to see (from brute force) that, for example, 3^2 - 5 = 22 = 27^2 (mod 10

Take the elliptic curve y^2 = x^3 - 5 that has no rational solutions [1]. But it's easy to see (from brute force) that, for example, 3^2 - 5 = 22 = 27^2 (mod 101). [1] https://kconrad.math.uconn.edu/blurbs/gradnumthy/mordelleqn1.pdf https://kconrad.math.uconn.edu/blurbs/gradnumthy/mordelleqn1...