## Dhaka regional higher secondary/8

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Ragib Farhat Hasan
Posts: 62
Joined: Sun Mar 30, 2014 10:40 pm

### Dhaka regional higher secondary/8

For all positive integers x,y; f(x) ≥ 0 and f(xy) = f(x) + f(y). If the digit at
the one’s of x is 6, then f(x) = 0. If f(1920) = 420 then f(2015) =?

asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm

### Re: Dhaka regional higher secondary/8

Prove that if \$5 \nmid x\$, then \$f(x)=0\$ using the first 2 conditions.

Ragib Farhat Hasan
Posts: 62
Joined: Sun Mar 30, 2014 10:40 pm

### Re: Dhaka regional higher secondary/8

But f(2015)=?

mdhasib
Posts: 10
Joined: Fri Jul 22, 2016 11:43 am

### Re: Dhaka regional higher secondary/8

I think F(2015)=420. Because F(5*384)=F(1920)=420=F(5)+F(384)=F(5) and F(384)=0 because 5 does not divide 384 . So F(2015)=F(5*13*31)=F(5)+F(13)+F(31)=F(5)=420