Introduction to number theory problems and solutions
Number theory is the branch of pure mathematics that concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into the several fields, according to the methods used and the type of questions investigated and let we about number theory problems and solutions. (Source – Wikipedia).
Number Theory Problems and Solutions
Example 1:
Find the solutions of consecutive numbers and the product of the number is 143
Solution:-
Let as assume the two consecutive numbers be x, x +1.
Where the product is 143 so,
X * (x + 1) = 143
x2 + x = 143
x2 + x – 143 = 0
x2 + 13x – 11x – 143 = 0
(x + 13) (x - 11) = 0
(x + 13) = 0 (or) (x - 11) = 0
x = -13 (or) x = 11
-13 is not possible to get 143
Therefore we take x = 11
So, x + 1 = 11 + 1 = 12
The consecutive numbers is 11 and 12.
Example 2:
Verify the given sequence described by an = 12n2 + 1 and A.P.?
Solution:
an = 12n2 + 1
a1 = 12(1)2 + 1 = 13,
a2 = 12(2)2 + 1 = 49
a3 = 12(3)2 + 1 = 109,
a4 = 12(4)2 + 1 = 193
The number theory problems solutions in sequence is 13, 49, 109, 193...
Here, 49 – 13 = 36
Example 3 :
Find the missed term in the given numbers 31, 29, ____, 25.
The above stated number is in descending order.
The known difference between the number 29 – 31 = 2.
Hence the given numbers are in descending order so we can subtract the numbers 2 from 29 means the answer is 27. I like to share this is 0 a natural number with you all through my article.
More Number Theory Problems and Solutions
Example 1:
Identify the type of numbers -7, 3 ÷ 4, `sqrt(8)`
Solution:
-7 - Integer
3 ÷ 4 - Fraction
`sqrt(8)` - Irrational Number
Example 2:
Mention the values of the consecutive numbers where the sum of the two numbers is 91.
Solution: Let we mention the two consecutive numbers be x, x+1.
Where the sum is 91 so,
x + x + 1 = 91
2x + 1 = 91
2x = 90
x = 45
Therefore, x + 1 = 45 + 1 = 46
So the number theory problems solutions of an consecutive numbers is 45 and 46.
The above problems are stated in number theory problems and solutions
Number theory is the branch of pure mathematics that concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into the several fields, according to the methods used and the type of questions investigated and let we about number theory problems and solutions. (Source – Wikipedia).
Number Theory Problems and Solutions
Example 1:
Find the solutions of consecutive numbers and the product of the number is 143
Solution:-
Let as assume the two consecutive numbers be x, x +1.
Where the product is 143 so,
X * (x + 1) = 143
x2 + x = 143
x2 + x – 143 = 0
x2 + 13x – 11x – 143 = 0
(x + 13) (x - 11) = 0
(x + 13) = 0 (or) (x - 11) = 0
x = -13 (or) x = 11
-13 is not possible to get 143
Therefore we take x = 11
So, x + 1 = 11 + 1 = 12
The consecutive numbers is 11 and 12.
Example 2:
Verify the given sequence described by an = 12n2 + 1 and A.P.?
Solution:
an = 12n2 + 1
a1 = 12(1)2 + 1 = 13,
a2 = 12(2)2 + 1 = 49
a3 = 12(3)2 + 1 = 109,
a4 = 12(4)2 + 1 = 193
The number theory problems solutions in sequence is 13, 49, 109, 193...
Here, 49 – 13 = 36
Example 3 :
Find the missed term in the given numbers 31, 29, ____, 25.
The above stated number is in descending order.
The known difference between the number 29 – 31 = 2.
Hence the given numbers are in descending order so we can subtract the numbers 2 from 29 means the answer is 27. I like to share this is 0 a natural number with you all through my article.
More Number Theory Problems and Solutions
Example 1:
Identify the type of numbers -7, 3 ÷ 4, `sqrt(8)`
Solution:
-7 - Integer
3 ÷ 4 - Fraction
`sqrt(8)` - Irrational Number
Example 2:
Mention the values of the consecutive numbers where the sum of the two numbers is 91.
Solution: Let we mention the two consecutive numbers be x, x+1.
Where the sum is 91 so,
x + x + 1 = 91
2x + 1 = 91
2x = 90
x = 45
Therefore, x + 1 = 45 + 1 = 46
So the number theory problems solutions of an consecutive numbers is 45 and 46.
The above problems are stated in number theory problems and solutions
