<h2>
Step-by-step explanation:</h2>
As per the question,
Let a be any positive integer and b = 4.
According to Euclid division lemma , a = 4q + r
where 0 ≤ r < b.
Thus,
r = 0, 1, 2, 3
Since, a is an odd integer, and
The only valid value of r = 1 and 3
So a = 4q + 1 or 4q + 3
<u>Case 1 :-</u> When a = 4q + 1
On squaring both sides, we get
a² = (4q + 1)²
= 16q² + 8q + 1
= 8(2q² + q) + 1
= 8m + 1 , where m = 2q² + q
<u>Case 2 :-</u> when a = 4q + 3
On squaring both sides, we get
a² = (4q + 3)²
= 16q² + 24q + 9
= 8 (2q² + 3q + 1) + 1
= 8m +1, where m = 2q² + 3q +1
Now,
<u>We can see that at every odd values of r, square of a is in the form of 8m +1.</u>
Also we know, a = 4q +1 and 4q +3 are not divisible by 2 means these all numbers are odd numbers.
Hence , it is clear that square of an odd positive is in form of 8m +1
Step-by-step explanation:
State you answer in the simplest form
Answer:
THANK YOU 505
Step-by-step explanation:
Answer:100%. Probability
Step-by-step explanation:
Emily = aa
Man = AA
After crossing the two, the result wI'll be Aa, Aa, Aa, Aa
Since every result has a carrier(a) in it, makes it 100% probability.
Answer:
The two numbers are 13 and 6.
Step-by-step explanation:
x+y=19
x-y=7
-----------
2x=26
x=26/2
x=13
13+y=19
y=19-13
y=6
x=13, y=6.
