48 lines
939 B
Ruby
48 lines
939 B
Ruby
require 'rational' # for lcm
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require 'mathn' # for prime_division
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def powerMod(b, p, m)
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result = 1
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bits = p.to_s(2)
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for bit in bits.split('')
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result = (result * result) % m
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if bit == '1'
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result = (result * b) % m
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end
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end
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result
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end
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def multOrder_(a, p, k)
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pk = p ** k
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t = (p - 1) * p ** (k - 1)
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r = 1
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for q, e in t.prime_division
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x = powerMod(a, t / q ** e, pk)
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while x != 1
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r *= q
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x = powerMod(x, q, pk)
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end
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end
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r
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end
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def multOrder(a, m)
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m.prime_division.inject(1) {|result, f|
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result.lcm(multOrder_(a, *f))
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}
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end
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puts multOrder(37, 1000) # 100
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b = 10**20-1
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puts multOrder(2, b) # 3748806900
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puts multOrder(17,b) # 1499522760
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b = 100001
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puts multOrder(54,b)
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puts powerMod(54, multOrder(54,b), b)
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if (1...multOrder(54,b)).any? {|r| powerMod(54, r, b) == 1}
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puts 'Exists a power r < 9090 where powerMod(54,r,b)==1'
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else
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puts 'Everything checks.'
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end
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