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(2) ax −By = 1, for example he proved that when max(a2, B) > 2.374 ·1010, the diophantine equation (2) has at most one integer solution. In fact, Ljunggren [4] proved this result without that restriction. (The author would like to express his gratitude to the referee for this reference.) The diophantine equation (2) includes many interesting special cases such as x4−By2 = 1, 4x4−By2 = 1 and 9x4 −By2 = 1. In the present note we will prove the following two results:

A note on the diophantine equation a2x4-By2=1

A note on the diophantine equation a²x⁴-By²=1