Suppose there are at least x peaches in this pile, lend them four, and it becomes x+4. Five monkeys took peaches A, B, C, D and E respectively (including one they ate), and they got it.

a=(x+4)/5，b=4(x+4)/25，c= 16(x+4)/ 125，d=64(x+4)/625，e=256(x+4)/3 125

E should be an integer, and 256 is not divisible by 5, so (x+4) should be a multiple of 3 125, so (x+4)=3 125k(k is a natural number). When k = 1, x=3 12 1.

So five monkeys picked at least 3 12 1 peach.

(3 12 1- 1)/5 * 4 = 2496 (2496- 1)/5*4= 1996 ( 1996-66)

(1596-1)/5 * 4 =1276 (unit) (1276-1)/5 * 4 =1020 (unit).

So in the end, 1020 remains.

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