Claims

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1962_01_01_lehmer_lehmer_mills_selfridge: Theorem 1 of Lehmer, Lehmer, Mills and Selfridge (Math. Comp. 16 (1962)) lists the thirteen primes with no three consecutive cubic residues and shows every other prime has such a run starting by 23532, sharp infinitely often.

1991_01_01_hildebrand: Theorem 1 of Hildebrand (Michigan Math. J. 38 (1991)) proves that for every k the least pair of consecutive kth power residues modulo p is bounded in p, so Lambda(k,2) is finite and the first question of Problem 436 is yes.

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