Tìm số tự nhiên nhỏ nhất biết rằng khi chia số đó cho 15,32,75 đều dư 2
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\(\frac{21^2.14.125}{35^3.6}\)
\(=\frac{7^2.3^2.2.7.5^3}{7^3.5^3.2.3}\)
\(=\frac{7^3.3^2.2.5^3}{7^3.5^3.2.3}\)
\(=3\)
Bo may la binh day k di hieu ashdbfgbgygygggydfsghuyfhdguuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu3
Bo may la binh day k di hieu ashdbfgbgygygggydfsghuyfhdguuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu3
Bo may la binh day k di hieu ashdbfgbgygygggydfsghuyfhdguuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu3
=a.1000+b.100+c.10+d-(a+b+c+d)
=a.999+a+b.99+b+c+9+c+d-(a+b+c+d)
=a.999+b.99+c.9
mà 999;99;9 đều chia hết 9 nên abcd-(a+b+c+d) chia hết 9
a) A = 1 + 3 + 32 + 33 + ...+ 335
=> 3A = 3 + 32 + 33 + 34 +...+ 336
=> 3A - A = 336 - 1
\(\Rightarrow A=\frac{3^{36}-1}{2}\)
b) ta có: A = 1 + 3 + 32 + 33 +...+ 335 ( có 36 số hạng)
A = (1+3) + (32 + 33) + ...+ (334 + 335) ( có 13 nhóm)
A = 4 + 32.(1+3) + ...+ 334.(1+3)
A = 4 + 32.4 + ...+ 334.4
A = 4.(1+32 +...+ 334) chia hết cho 4
..
phần còn lại bn làm tương tự nha! phần b bn nhóm 3 số hạng lại vs nhau, xog làm như trên là ra !
Gọi số đó là abc
Theo bài ra ta có cba-abc=792
(100c+10b+a)-(100a+10b+c)=792
100c+10b+a-100a-10b-c=792
99c-99a=792
99(c-a)=792
c-a=8
mà c:a=3
3a-a=8
2a=8
a=4; c=12(vô lý)
Không có abc
Chứng minh 1994 mũ 100 - 1 và 1994 mũ 100 + 1 không đồng thời là số nguyên tố
1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1000
= 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1000
= 1000
Bo may la binh day k di hieu ashdbfgbgygygggydfsghuyfhdguuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu3
Ta gọi số cần tìm là a
Ta có:a:15 dư 2 ---> a-2 chia hết(dấu) cho 15
a:32 dư 2----> a-2 chia hết cho 32
a:75 dư 2----->a-2 chia hết cho 75
Suy ra a thuộc BC{15,32,75}
Ta có: 15 = 3.5
32=25.1
75=3.52
BCNN(15,32,75)=3.25.52=1200
Suy ra a-5 thuộc B(1200)
Suy ra a-5 thuộc(1200 , 2400, 3600,4800,...)
Suy ra a thuộc(1202,2402,3602,4802,...)
Do a nhỏ nhất nên a =1202
Vậy số đó là:1202