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Description
The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary MathematicsThis book contains 320 unconventional problems in algebra, arithmetic, elementary number theory, and trigonometry. Most of the problems first appeared in competitive examinations sponsored by the School Mathematical Society of the Moscow State University and the Mathematical Olympiads held in Moscow. Although most of the problems presuppose only high school mathematics, they are not easy; some are of uncommon difficulty and will challenge the
This book contains 320 unconventional problems in algebra, arithmetic, elementary number theory, and trigonometry. Most of the problems first appeared in competitive examinations sponsored by the School Mathematical Society of the Moscow State University and the Mathematical Olympiads held in Moscow. Although most of the problems presuppose only high school mathematics, they are not easy; some are of uncommon difficulty and will challenge the ingenuity of any research mathematician. Nevertheless, many are well within the reach of motivated high school students and even advanced seventh and eighth graders.The problems are grouped into twelve separate sections. Among these are: the divisibility of integers, equations having integer solutions, evaluating sums and products, miscellaneous algebraic problems, the algebra of polynomials, complex numbers, problems of number theory, distinctive inequalities, difference sequences and sums, and more.
Complete solutions to all problems are given; in many cases, alternate solutions are detailed from different points of view. Solutions to more advanced problems are given in considerable detail. Moreover, when advanced concepts are employed, they are discussed in the section preceding the problems. Useful in a variety of ways in high school and college curriculums, this challenging volume will be of particular interest to teachers dealing with gifted and advanced classes.
Binding Type: Paperback
Publisher: Dover Publications
Published: 09/28/1993
ISBN: 9780486277097
Pages: 480
Weight: 1.03lbs
Size: 8.76h x 5.16w x 0.90d
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Product Reviews
★★★★★ 5
No problems after a year and a half
Color: Dogwood & Calming, Size: Medium
Have been regularly buying these for my corgi for about a year and a half. The 2 pack lasts about a month or 2 each time. Pieces break off in small enough pieces that they safely pass through his digestive system. He gnaws each one down to about 1/4 the original size before we take it away and give him a new one. He continues to have regular bowel movements and has a healthy appetite so I can’t imagine any problems arising after so long.
I have tried other alternatives and every other similar chew breaks off in larger pieces and didn’t feel comfortable letting him chew/eat them. I noticed there are a few 1 star reviews saying their dogs got sick off these but after a year and a half I have had 0 issues with this product. I guess it depends on the dog and how big of pieces they are swallowing. My dog ingests pieces about the size of a grain of rice so just pay attention and you should be fine.
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Reviewed in the United States on February 18, 2026
★★★★★ 5
Long lasting and safer alternative to sticks
Color: Dogwood & Calming, Size: Medium
These are great, very durable, and have lasted a very long time. Much safer for my dogs than the random sticks they find in the yard. They do get shorter with chewing eventually, but they don't break off in little chunks like I've seen with some nylon chews, and they don't splinter like wood. Medium size works well for both my 16 lb Cavalier and my 60 lb Pyrenees/Golden mix. They're both moderate-to-aggressive chewers, though size obviously affects how much damage they can do.
I wish you could buy the hemp chew separately because that one is very much a favorite in my house, so after 2 years and 2 purchases, I have barely any left of the remaining hemp chew, but still 2 of the dogwood chews that neither dog is as interested in anymore. I'd love to buy a couple more of just the hemp one.
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Reviewed in the United States on April 30, 2026
★★★★★ 5
Your dog will thank you.
Color: Dogwood & Fresh Breath, Size: Large
My dogs loves to chew on these. They make a small mess but not as bad as other chews. They are food for keeping teeth clean.
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Reviewed in the United States on May 31, 2026
★★★★★ 5
Nice chew toy
Color: Dogwood Mushroom, Size: Medium, Color: Dogwood Mushroom, Size: Medium
Super durable and puppy loves it. It was a bit hard for her at first but now at 5 months it’s one of her favorite things to gnaw on! It is heavy for the size but seems to be great quality and has given many hours of chew time with minimal wear.
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Reviewed in the United States on March 12, 2026
★★★★★ 4
Long lasting
Color: Dogwood & Calming, Size: Medium
My dogs love these bones.
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Reviewed in the United States on March 25, 2026