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葛立恒数的最后n位
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// https://www.zhihu.com/question/372790433/answer/2873612363 | |
// a 代表基数,m 代表被余数, t初始值表示m中0的个数(即因子5的个数) | |
function my_tetration_mod (a, t, m) { | |
if (m === 2n) return a % 2n | |
let phi_m // phi(m) 为欧拉函数,表示小于m且与m互质的自然数个数 | |
if (t > 0) { | |
phi_m = m * 2n / 5n | |
} else { | |
phi_m = m / 2n | |
} | |
const pow = my_tetration_mod(a, t - 1, phi_m) + phi_m | |
return pow_mod(a, pow, m) | |
} | |
const digits = 100 | |
console.log(my_tetration_mod(3n, digits, BigInt(`1${'0'.repeat(digits)}`))) // 9404248265018193851562535796399618993967905496638003222348723967018485186439059104575627262464195387n | |
// https://gist.github.com/krzkaczor/0bdba0ee9555659ae5fe | |
// console.log(pow_mod(3n, 587n, 1000n)) // 387 | |
function pow_mod (base, pow, divisor) { | |
let result = 1n | |
let x = base % divisor | |
while (pow > 0n) { | |
if (pow % 2n === 1n) { | |
result *= x | |
result %= divisor | |
} | |
pow /= 2n | |
x *= x | |
x %= divisor | |
} | |
return result | |
} |
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