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4

Part of 1999 South africa National Olympiad

Problems(1)

L(p) - 1 is divisible by p if p is prime

Source: South Africa 1999

9/30/2005
The sequence L1, L2, L3, …L_1,\ L_2,\ L_3,\ \dots is defined by L1=1,  L2=3,  Ln=Ln−1+Ln−2 for n>2. L_1 = 1,\ \ L_2 = 3,\ \ L_n = L_{n - 1} + L_{n - 2}\textrm{ for }n > 2. Prove that Lp−1L_p - 1 is divisible by pp if pp is prime.
number theorynumber theory solved