Then x * x =100000 * y+X.
x*x-x = 100000*y
x*(x- 1)= 100000*y
y=(x*x-x)/ 100000=x*(x- 1)/(2^5*5^5)
X is a multiple of 5 = 3 125 (because X is a five-digit number, it cannot be a multiple of 10 5 = 100000).
Let x=3 125k (k is a natural number).
Then 3125k * (3125k-1) =100000 * y.
(3 125k- 1) is a multiple of 2 5 = 32.
Let (3 125k- 1) =32m (m is a natural number).
m =(3 125k- 1)/32 = 98k-( 1 1k+ 1)/32
Let (11k+1)/32 = n (n is a natural number).
rule
k =(32n- 1)/ 1 1 = 3n-(n+ 1)/ 1 1
N =-1+11c (c is a natural number)
n=- 1 k=-3
n= 10 k=30- 1=29,x=90625
n=2 1 k=63-2=6 1,x = 190625 & gt; 100000 give up
N=32 k=96-3=93, x = 290625 & gt 100000 give up.
So x=90625
A=9,B=0,C=6,D=2,E=5