# Các bài toán số học trong đề thi APMOPS 2010

**Posted:**September 21, 2013

**Filed under:**APMOPS Leave a comment

* Question 1*: Find the last digit of the number (859435 of 2’s).

* Solution*: It is easy to prove by induction that the last digit of the number having the form is 8. Hence, the last digit of the number given in the question is 8.

* Question 2:* Find the value of

* Solution:* Remember that for any natural number , we always have

Thus,

* Question 3*: Find the smallest whole number that is not a factor of

* Solution:* We just need to consider these five numbers: 24, 25, 26, 27, 28, 29 (29 is a prime number).

Notice that 24=4.6 ; 25=5.5 ; 26=2.13 ; 27=3.9 ; 28=4.7 ; Hence 29 is our result.