YASH CLASSES
1. REAL
NUMBERS [ X ]
1. Express each of the following integers as a
product
of its prime
factors :
a. 945
b. 1025 c.
3025 d. 2589
e. 9872
f. 4521 g. 12000
h. 32587
i. 320158
j. 65987 k. 25814 l.102489
2. Show
that any positive odd
integer is the
4q + 1
and 4q + 3
where q integer .
3. Show
that any positive odd
integer is the
5q + 1
and 5q + 3
where q integer .
4. Show
that any positive even integer
is the
4q and 4q + 2
where q integer .
5. Prove that 3m , 3m + 1 the square of any
integers
but not the form of 3m + 2 .
6.Prove that 9m , 9m + 1and 9m + 4 the square of
any integers but not the form of 9m + 5 .
7. Prove that 5m , 5m + 1and 5m + 4 the square of
any integers but not the form of 5m + 3 .
8. Prove that 5m and 5m + 1 the cube of
any
integers
but not the form of 5m + 2 and 5m
+ 3 .
9. Prove that 4m and 4m + 1
the cube of any
integers
but not the form of 4m + 2 and 4m
+ 3 .
10. Prove that
one of every three consecutive
positive
integers is divisible by 3 .